Let `f: RvecR` be a continuous function which satisfies `f(x)=` `int_0^xf(t)dtdot` Then the value of `f(1n5)` is______

Let f be a continuous function on R such that f (1/(4n))=sin e^n/(e^(n^2))+n^2/(n^2+1) Then the value of f(0) is

Let f:[1,oo) to [2,oo) be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is

A function satisfying int_0^1f(tx)dt=nf(x) , where x>0 is

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be